The 2006 SMH HSC Study Guide is out today.
Here's what they said about Mathematics Extension 2:
The Extension 2 paper consists of eight questions, each worth 15 marks. It is important to manage your time well. Remember to use the fact that the numbered sub-parts of a question are often related. Watch for keywords: hence suggests that "using this result is the best way to do it" (following on from the last part), deduce means "prove, using logical steps, but it should come out easily", describe needs the use of words and state indicates that you need to write the result. Always use the number of marks allocated to a part of the question as a guide to the amount of work expected.
A thorough understanding of the Mathematics and Extension 1 courses is required, as the Extension 2 course builds on previous work. The difference in levels of achievement can be seen in the Performance Bands. In Band E2, a student typically "solves standard problems from the Mathematics Extension 2 topic areas such as integration and complex numbers". It is expected that a Band E3 student "solves problems from the Mathematics Extension 2 topic areas, such as complex numbers, volumes, polynomials, conics and mechanics", while a Band E4 student "synthesises mathematical techniques, results and ideas creatively across the Mathematics, Mathematics Extension 1 and Mathematics Extension 2 courses to solve problems" and "combines excellent algebraic and modelling skills, multi-step logic and mathematical insight to solve difficult problems".
Techniques of integration are often assessed in the first question. Remember that the process of integration by parts comes from integrating the product rule, sometimes written in a shortened form as d(uv)=udv+vdu. Take care with integrals involving completing the square, particularly if the term in x<sup>2</sup> is negative. When using partial fractions, if you are asked to find values for a and b in part (i) and you can't, use any values of a and b to obtain marks for the correct process in part (ii).
The question on complex numbers generally builds from basic operations to a more detailed understanding of the geometrical representation of complex numbers. When sketching a region on the Argand diagram, mark the axes, scale, intercepts and other significant features clearly. To assess your understanding of this content area, try some tutorials on NSW HSC Online ( http://hsc.csu.edu.au/maths/ext2/complex_numbers/ ).
Your sketching of curves should involve large diagrams with important features such as axes, asymptotes, turning points and intercepts clearly labelled. Building up the shape of the graph is best done in stages but make sure that your final answer is obvious to the marker.
Understanding the terminology helps achieve good marks in a conics question. The topic of implicit differentiation is part of this course because it is the easiest way to derive the equation of the tangent to a conic expressed in implicit form. Do not waste time deriving equations already given in the question.
For questions based on harder Extension 1 circle geometry; copy the diagram into your exam booklet. There is no point writing on the diagram on the examination paper as the HSC marker will not see this. Use the copy of the diagram you have created in your exam booklet to define additional pronumerals. Keywords such as prove and show indicate that you need to give clear, coherent reasons using correct terminology.
When working with questions involving inequalities, make sure that you don't start with the inequality you are trying to prove. For further practice with harder Extension 1 topics, try NSW HSC Online ( http://hsc.csu.edu.au/maths/ext2/hard_topics/ ).
The more challenging questions often occur later in the paper. However, later questions frequently contain parts that
are straightforward, so make sure that you allow time to attempt them.
Here's what they said about Mathematics Extension 2:
The Extension 2 paper consists of eight questions, each worth 15 marks. It is important to manage your time well. Remember to use the fact that the numbered sub-parts of a question are often related. Watch for keywords: hence suggests that "using this result is the best way to do it" (following on from the last part), deduce means "prove, using logical steps, but it should come out easily", describe needs the use of words and state indicates that you need to write the result. Always use the number of marks allocated to a part of the question as a guide to the amount of work expected.
A thorough understanding of the Mathematics and Extension 1 courses is required, as the Extension 2 course builds on previous work. The difference in levels of achievement can be seen in the Performance Bands. In Band E2, a student typically "solves standard problems from the Mathematics Extension 2 topic areas such as integration and complex numbers". It is expected that a Band E3 student "solves problems from the Mathematics Extension 2 topic areas, such as complex numbers, volumes, polynomials, conics and mechanics", while a Band E4 student "synthesises mathematical techniques, results and ideas creatively across the Mathematics, Mathematics Extension 1 and Mathematics Extension 2 courses to solve problems" and "combines excellent algebraic and modelling skills, multi-step logic and mathematical insight to solve difficult problems".
Techniques of integration are often assessed in the first question. Remember that the process of integration by parts comes from integrating the product rule, sometimes written in a shortened form as d(uv)=udv+vdu. Take care with integrals involving completing the square, particularly if the term in x<sup>2</sup> is negative. When using partial fractions, if you are asked to find values for a and b in part (i) and you can't, use any values of a and b to obtain marks for the correct process in part (ii).
The question on complex numbers generally builds from basic operations to a more detailed understanding of the geometrical representation of complex numbers. When sketching a region on the Argand diagram, mark the axes, scale, intercepts and other significant features clearly. To assess your understanding of this content area, try some tutorials on NSW HSC Online ( http://hsc.csu.edu.au/maths/ext2/complex_numbers/ ).
Your sketching of curves should involve large diagrams with important features such as axes, asymptotes, turning points and intercepts clearly labelled. Building up the shape of the graph is best done in stages but make sure that your final answer is obvious to the marker.
Understanding the terminology helps achieve good marks in a conics question. The topic of implicit differentiation is part of this course because it is the easiest way to derive the equation of the tangent to a conic expressed in implicit form. Do not waste time deriving equations already given in the question.
For questions based on harder Extension 1 circle geometry; copy the diagram into your exam booklet. There is no point writing on the diagram on the examination paper as the HSC marker will not see this. Use the copy of the diagram you have created in your exam booklet to define additional pronumerals. Keywords such as prove and show indicate that you need to give clear, coherent reasons using correct terminology.
When working with questions involving inequalities, make sure that you don't start with the inequality you are trying to prove. For further practice with harder Extension 1 topics, try NSW HSC Online ( http://hsc.csu.edu.au/maths/ext2/hard_topics/ ).
The more challenging questions often occur later in the paper. However, later questions frequently contain parts that
are straightforward, so make sure that you allow time to attempt them.
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